Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon's descent algebra and another using random walk on chambers of hyperplane arrangements. These coincide for types ,,,, and rank two groups but not always. Both notions have the same simple eigenvalues. The hyperplane definition is especially natural and satisfies a positivity property when is crystallographic and the relevant parameter is a good prime. The hyperplane viewpoint suggests deep connections with Lie theory and leads to a notion of riffle shuffling for arbitrary real hyperplane arrangements and oriented matroids.